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Ordering decimals through thousandths

Learn all about comparing decimals. It teaches students how to order decimals from least to greatest by comparing each place value, starting from the most significant and moving to the right.

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Video transcript

- [Instructor] So we have four numbers listed here, and what I would like you to do is get out some pencil and paper and pause this video and see if you can order these numbers from least to greatest. So the least would be at the left, and then keep going greater, and greater, and greater until you get to the greatest number. So pause the video and have a go at that. All right, now let's tackle this together. And the way that I like to do it is I start at the, I guess you could say, the most significant place value or the largest place value, compare the numbers. And then keep moving to the right to smaller and smaller place values. So we can start in the ones place. This number has zero ones, this number has zero ones, this number has zero ones, and that number has zero ones. So the ones place really doesn't help us much. But then we can move to the tenths place. This number has 7/10. This number has 0/10, so just from that we know that the second number is less than the first number. This has 7/10, this has 0/10. It doesn't matter what's happening in the places after that, to the right of that. This number over here also has 7/10, just like the first number. And this last number also has 7/10. So we know from comparing the ones and then the tenths place is that this number right over here is the smallest of the four numbers. They all have zero ones, but this one also has 0/10. So I'll list that here, 0.074. Now let's move to the hundredths place. So this number has 0/100. We've already used this number. This number has 7/100. And then this number, it might not be obvious, but the hundredths place you can view as being zero, the hundredths place, you can just put a zero there and not change the value. So this also has 0/100. So these three numbers, same ones, same tenths, but this number, 0.77, has 7/100, while the other two had 0/100. So this is going to be the largest of our four numbers. This is larger than these other two because of what we see in the hundredths place. It doesn't matter what's happening in the thousandths place or anything beyond that. So we put the 0.77 right over there. And now we are tasked, and we've used this number, and now we have to compare these two numbers, which were equal in the ones, tenths, and hundredths place, so we have to go to the thousandths place. This number has 7/1000. This number has 0/1000. So this number is smaller than this first number here. So I'll write this next, 0.7, and then the third smallest, or the next to largest number is this one over here, 0.707, and we're done. So the main idea is you wanna compare the most significant place values, the largest places values first, and then based on that, keep moving to the right to compare less and less significant place values.